We show that the efficient excitation energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions is fueled by underdamped vibrations of the embedding proteins. For this, we present numerically exact resul
ts for the quantum dynamics of the excitons in the presence of nonadiabatic vibrational states in the Fenna-Matthews-Olson aggregate employing a environmental fluctuation spectral function derived from experiments. Assuming the prominent 180 cm$^{-1}$ vibrational mode to be underdamped, we observe, on the one hand, besides vibrational coherent oscillations between different excitation levels of the vibration also prolonged electronic coherent oscillations between the initially excited site and its neighbours. On the other hand, however, the underdamped vibrations provide additional channels for the excitation energy transfer and by this increase the transfer speed by up to $30%$ .
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starti
ng from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fullfills a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.
